{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "s(t)=(x*w)(t)=\\sum_{a=-\\infty}^{a=\\infty} x(a)w(t-a)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def true_position(t):\n",
    "    return 10 * np.sin(0.1 * t)\n",
    "\n",
    "def observation(t):\n",
    "    return true_position(t) + noise(t)\n",
    "\n",
    "def noise(t):\n",
    "    return np.random.normal(loc=0, scale=1)\n",
    "\n",
    "def w(t):\n",
    "    if t < 0 and t > 5:\n",
    "        return 0\n",
    "    else:\n",
    "        return 5-t\n",
    "# 定义时间序列\n",
    "t = np.arange(0, 200, 0.5)\n",
    "\n",
    "# 生成多个观测结果\n",
    "observations = np.array([observation(ti) for ti in t])\n",
    "# mean\n",
    "obs_mean = np.mean(observations.reshape(-1, 5), axis=1)\n",
    "t_mean = np.mean(t.reshape(-1, 5), axis=1)\n",
    "# convolution\n",
    "window_size = 20\n",
    "kernel = np.ones(window_size) / window_size\n",
    "smoothed_observations = np.convolve(observations, kernel, mode='same')\n",
    "# 绘制真实位置和观测结果曲线\n",
    "plt.plot(t, true_position(t), label='True Position')\n",
    "plt.scatter(t, observations, s=1, label='Observations')\n",
    "plt.plot(t_mean, obs_mean, label='mean Observations')\n",
    "plt.plot(t, smoothed_observations, label='smoothed_observations')\n",
    "\n",
    "# 设置图形标题和标签\n",
    "plt.title('Laser Sensor Observations')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.legend()\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
